# Weil-\'{e}tale cohomology and duality for arithmetic schemes in negative weights

@inproceedings{Beshenov2020WeiletaleCA, title={Weil-\'\{e\}tale cohomology and duality for arithmetic schemes in negative weights}, author={Alexey Beshenov}, year={2020} }

Flach and Morin constructed in [9] Weil-étale cohomology H i W,c(X,Z(n)) for a proper, regular arithmetic scheme X (i.e. separated and of finite type over SpecZ) and n ∈ Z. In the case when n < 0, we generalize their construction to an arbitrary arithmetic scheme X, thus removing the proper and regular assumption. The construction assumes finite generation of suitable étale motivic cohomology groups.

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